Details

analyze1.0s

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
6.2%	90.4%	3.4%	6
6.2%	90.4%	3.4%	7
6.2%	88.8%	5%	8
7.8%	77.9%	14.3%	9
7.8%	56.5%	35.7%	10
7.8%	56.5%	35.7%	11
8.1%	41.5%	50.3%	12
8.3%	41.4%	50.3%	13
8.4%	40.2%	51.4%	14

sample100.0ms

Algorithm

intervals

Results

32.0ms	447×	body	80	nan
19.0ms	256×	body	80	valid
15.0ms	203×	body	80	invalid

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	32	10
1	65	10
2	181	8
3	522	8
4	2203	8
5	5002	8

prune32.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.2b

Counts

2 → 2

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
1.1b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.1b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`add-exp-log` `log-prod`
10×	`pow1` `add-log-exp`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`exp-prod`
3×	`times-frac` `exp-sum` `prod-exp` `associate-/r*` `cbrt-unprod` `rem-exp-log`
2×	`cbrt-undiv` `exp-diff` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `log-pow` `-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`sub-neg` `flip3--` `frac-2neg` `associate-r/` `associate--l+` `clear-num` `sum-log` `flip--` `div-inv` `associate-/l/` `associate-/l`

Counts

4 → 95

Calls

4 calls:

13.0ms	(* (- t 1.0) (log a))
8.0ms	(* y (log z))
10.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
20.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series209.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (- t 1.0) (log a))
7.0ms	(* y (log z))
64.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
129.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify89.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	569	965
1	2353	793
2	5001	726

prune209.0ms

Filtered

75 candidates to 107 candidates (-42.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	103	4	107
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	104	5	109

Merged error: 0.0b

Counts

109 → 5

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))))
0.2b	(* (log (/ 1 a)) t)
0.3b	(* (log (/ 1 z)) y)
1.1b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))) y)

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
82×	`add-sqr-sqrt` `associate-r`
62×	`*-un-lft-identity`
61×	`add-cube-cbrt`
55×	`unpow-prod-down`
45×	`add-exp-log`
24×	`div-exp`
22×	`add-cbrt-cube`
17×	`exp-sum`
16×	`prod-exp`
15×	`associate-l`
14×	`pow1`
8×	`distribute-lft-neg-out` `log-rec` `pow-exp` `unswap-sqr`
6×	`log-pow` `cbrt-unprod` `div-inv`
5×	`cbrt-undiv` `sqr-pow`
4×	`exp-diff` `associate-/r/` `add-log-exp`
3×	`pow-prod-down` `associate-/r` `-commutative`
2×	`pow-to-exp` `associate-+r-` `rec-exp` `distribute-neg-out` `pow-flip` `1-exp` `associate-*r/` `unsub-neg` `inv-pow`
1×	`frac-2neg` `clear-num` `associate-/l/` `associate-/l*`

Counts

4 → 177

Calls

4 calls:

51.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))))
8.0ms	(* (log (/ 1 a)) t)
8.0ms	(* (log (/ 1 z)) y)
33.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))) y)

series277.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))))
10.0ms	(* (log (/ 1 a)) t)
12.0ms	(* (log (/ 1 z)) y)
132.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))) y)

simplify113.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1050	2460
1	4978	2167
2	5002	2167

prune539.0ms

Filtered

131 candidates to 189 candidates (-44.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	185	4	189
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	189	5	194

Merged error: 0.0b

Counts

194 → 5

localize49.0ms

Local error

Found 4 expressions with local error:

1.1b	(/ (* (* (cbrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))))) (cbrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))))) (cbrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))))) y)
2.0b	(cbrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))))
2.0b	(cbrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))))
2.0b	(cbrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

18×	`associate-*r/`
15×	`cbrt-div`
13×	`add-exp-log`
9×	`add-cbrt-cube`
7×	`associate-/l/`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`frac-times` `associate-*l/`
4×	`pow1` `add-log-exp`
3×	`cbrt-undiv` `cbrt-prod` `times-frac` `pow1/3` `div-exp` `prod-exp` `associate-/r*` `cbrt-unprod`
1×	`frac-2neg` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 60

Calls

4 calls:

17.0ms	(/ (* (* (cbrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))))) (cbrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))))) (cbrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))))) y)
28.0ms	(cbrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))))
27.0ms	(cbrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))))
24.0ms	(cbrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))))

series813.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(/ (* (* (cbrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))))) (cbrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))))) (cbrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))))) y)
216.0ms	(cbrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))))
203.0ms	(cbrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))))
197.0ms	(cbrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))))

simplify63.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	534	2362
1	1816	1763
2	5001	1535

prune486.0ms

Filtered

65 candidates to 72 candidates (-10.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	71	6	77

Merged error: 0b

Counts

77 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))) y)
0.2b	(* (log (/ 1 a)) t)
0.3b	(* (log (/ 1 z)) y)
1.2b	(* x (/ (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))) y))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

1197×	`times-frac`
542×	`add-sqr-sqrt`
514×	`*-un-lft-identity`
513×	`add-cube-cbrt`
367×	`unpow-prod-down`
238×	`associate-r`
119×	`exp-sum`
76×	`associate-/l*`
45×	`add-exp-log`
44×	`distribute-lft-neg-out` `log-rec`
37×	`div-inv`
30×	`div-exp`
29×	`sqr-pow`
28×	`exp-diff` `associate-/r/`
22×	`add-cbrt-cube`
15×	`associate-l`
14×	`pow1` `associate-+r-` `distribute-neg-out` `unsub-neg`
10×	`prod-exp`
9×	`unswap-sqr`
8×	`pow-exp`
6×	`cbrt-undiv` `log-pow`
5×	`cbrt-unprod`
4×	`add-log-exp`
3×	`pow-prod-down` `associate-/r` `-commutative`
2×	`pow-to-exp` `rec-exp` `pow-flip` `1-exp` `inv-pow`
1×	`frac-2neg` `associate-*r/` `clear-num` `associate-/l/`

Counts

4 → 634

Calls

4 calls:

32.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))) y)
5.0ms	(* (log (/ 1 a)) t)
4.0ms	(* (log (/ 1 z)) y)
68.0ms	(* x (/ (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))) y))

series327.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))) y)
12.0ms	(* (log (/ 1 a)) t)
13.0ms	(* (log (/ 1 z)) y)
159.0ms	(* x (/ (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))) y))

simplify160.0ms

Algorithm

egg-herbie

Counts

646 → 646

Iterations

Useful iterations: 1 (46.0ms)

Iter	Nodes	Cost
0	2626	12259
1	5002	11830

prune2.9s

Filtered

472 candidates to 646 candidates (-36.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	646	0	646
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	646	6	652

Merged error: 0b

Counts

652 → 6

regimes804.0ms

Accuracy

85.8% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 1.4b

bsearch1.4s

Steps

Iters	Range		Point
5	1.3076417168438274e-89	3.009991245524962e-89	2.3650229309095837e-89

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	59
1	38	59

end0.0ms

analyze904.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
6.2%	90.4%	3.4%	6
6.2%	90.4%	3.4%	7
6.2%	88.8%	5%	8
7.8%	77.9%	14.3%	9
7.8%	56.5%	35.7%	10
7.8%	56.5%	35.7%	11
8.1%	41.5%	50.3%	12
8.3%	41.4%	50.3%	13
8.4%	40.2%	51.4%	14

sample3.3s

Algorithm

intervals

Results

998.0ms	14043×	body	80	nan
672.0ms	8000×	body	80	valid
590.0ms	7139×	body	80	invalid

Details

analyze1.0s

sample100.0ms

simplify68.0ms

prune32.0ms

localize36.0ms

rewrite57.0ms

series209.0ms

simplify89.0ms

prune209.0ms

localize32.0ms

rewrite110.0ms

series277.0ms

simplify113.0ms

prune539.0ms

localize49.0ms

rewrite100.0ms

series813.0ms

simplify63.0ms

prune486.0ms

localize23.0ms

rewrite181.0ms

series327.0ms

simplify160.0ms

prune2.9s

regimes804.0ms

bsearch1.4s

simplify2.0ms

end0.0ms

analyze904.0ms

sample3.3s

Profiling