Details

sample265.0ms

Algorithm

intervals

Results

137.0ms	1404×	body	80	nan
51.0ms	448×	body	80	valid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	33	10
1	73	10
2	197	8
3	558	8
4	2287	8
5	5001	8

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
0.7b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
0.8b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`add-exp-log` `log-prod` `exp-sum`
10×	`pow1` `add-log-exp`
9×	`prod-diff`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`exp-prod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`times-frac` `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 → 112

Calls

4 calls:

11.0ms	(* (- t 1.0) (log a))
4.0ms	(* y (log z))
80.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
35.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

series140.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (- t 1.0) (log a))
7.0ms	(* y (log z))
73.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
48.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

simplify61.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	580	1143
1	2309	897
2	5002	860

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
0.1b	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.1b	(fma (log (/ 1 a)) t b)
0.7b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
74×	`add-sqr-sqrt`
72×	`associate-r`
58×	`*-un-lft-identity`
57×	`add-cube-cbrt`
55×	`unpow-prod-down`
41×	`add-exp-log`
24×	`div-exp`
19×	`fma-udef`
18×	`add-cbrt-cube`
17×	`exp-sum`
14×	`prod-exp`
8×	`pow-exp`
6×	`pow1` `div-inv` `unswap-sqr`
5×	`cbrt-undiv` `sqr-pow`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r*`
2×	`pow-to-exp` `rec-exp` `1-exp` `associate-*r/`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `associate-/l/` `associate-/l`

Counts

4 → 153

Calls

4 calls:

37.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
0.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.0ms	(fma (log (/ 1 a)) t b)
13.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

series311.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
24.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
13.0ms	(fma (log (/ 1 a)) t b)
138.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

simplify95.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	904	2177
1	4142	1910
2	5001	1900

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (log (/ 1 a)) t b)
0.1b	(fma (log (/ 1 a)) t b)
0.1b	(fma (log (/ 1 a)) t b)
0.7b	(/ (* (/ x (* (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (/ (pow (/ (sqrt 1) a) 1.0) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-exp-log`
41×	`div-exp`
26×	`add-cbrt-cube`
20×	`prod-exp`
14×	`cbrt-undiv`
8×	`cbrt-unprod`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `pow-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `times-frac` `associate-/r*` `fma-udef` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 75

Calls

4 calls:

0.0ms	(fma (log (/ 1 a)) t b)
0.0ms	(fma (log (/ 1 a)) t b)
0.0ms	(fma (log (/ 1 a)) t b)
33.0ms	(/ (* (/ x (* (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (/ (pow (/ (sqrt 1) a) 1.0) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

series179.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(fma (log (/ 1 a)) t b)
13.0ms	(fma (log (/ 1 a)) t b)
13.0ms	(fma (log (/ 1 a)) t b)
140.0ms	(/ (* (/ x (* (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (/ (pow (/ (sqrt 1) a) 1.0) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

simplify64.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	543	1971
1	2281	1548
2	5001	1447

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
0.7b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (* (cbrt y) (cbrt y)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log`
32×	`div-exp`
22×	`prod-exp`
19×	`add-cbrt-cube`
9×	`cbrt-prod`
8×	`cbrt-undiv` `pow-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `cbrt-unprod`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`pow-to-exp` `rec-exp` `1-exp`
1×	`frac-2neg` `times-frac` `associate-r/` `clear-num` `associate-/r` `div-inv` `associate-/l/` `associate-/l*`

Counts

4 → 77

Calls

4 calls:

0.0ms	(cbrt y)
0.0ms	(cbrt y)
0.0ms	(cbrt y)
17.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (* (cbrt y) (cbrt y)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(cbrt y)
10.0ms	(cbrt y)
10.0ms	(cbrt y)
201.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (* (cbrt y) (cbrt y)))

simplify54.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	496	983
1	2103	774
2	5002	741

prune1.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes1.1s

Accuracy

0% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 1.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	32
1	27	32

end0.0ms

sample8.4s

Algorithm

intervals

Results

4.5s	46228×	body	80	nan
1.7s	15342×	body	80	valid