Details

sample194.0ms

Algorithm

intervals

Results

89.0ms	1343×	body	80	nan
33.0ms	440×	body	80	valid

simplify50.0ms

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

prune10.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 0.1b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
0.9b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.1b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite37.0ms

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:

7.0ms	(* (- t 1.0) (log a))
5.0ms	(* y (log z))
10.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
12.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series381.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (- t 1.0) (log a))
35.0ms	(* y (log z))
122.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
165.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify63.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (52.0ms)

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

prune356.0ms

Filtered

124 candidates to 89 candidates (71.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	119	5	124
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	121	5	126

Merged error: 0.0b

Counts

126 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

116×	`times-frac`
65×	`unpow-prod-down`
64×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
33×	`add-exp-log`
24×	`div-exp`
20×	`fma-udef`
18×	`exp-sum` `associate-/l*`
15×	`add-cbrt-cube`
8×	`pow-exp`
7×	`prod-exp` `associate-/r*` `div-inv`
5×	`cbrt-undiv` `sqr-pow`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `rec-exp` `frac-2neg` `1-exp` `clear-num` `cbrt-unprod`
1×	`associate-*r/` `associate-/l/`

Counts

4 → 159

Calls

4 calls:

9.0ms	(/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))
1.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
1.0ms	(fma (log (/ 1 a)) t b)
17.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

series754.0ms

Counts

4 → 12

Calls

4 calls:

276.0ms	(/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))
80.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
74.0ms	(fma (log (/ 1 a)) t b)
324.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

simplify77.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	746	2775
1	2943	2527
2	5003	2512

prune591.0ms

Filtered

171 candidates to 121 candidates (70.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	171	5	176

Merged error: 0.0b

Counts

176 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (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)
5.0b	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (/ y x))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

3162×	`times-frac`
1273×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
793×	`unpow-prod-down`
258×	`fma-udef`
256×	`exp-sum`
150×	`div-inv`
89×	`associate-/l*`
61×	`sqr-pow`
45×	`add-exp-log` `div-exp`
18×	`add-cbrt-cube`
17×	`associate-/r*`
12×	`pow-exp`
9×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `rec-exp` `1-exp`
2×	`frac-2neg` `clear-num`
1×	`associate-/r/` `associate-/l/`

Counts

4 → 1181

Calls

4 calls:

9.0ms	(/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))
1.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
1.0ms	(fma (log (/ 1 a)) t b)
42.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (/ y x))

series1.1s

Counts

4 → 12

Calls

4 calls:

274.0ms	(/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))
77.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
68.0ms	(fma (log (/ 1 a)) t b)
683.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (/ y x))

simplify312.0ms

Algorithm

egg-herbie

Counts

1193 → 1193

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5001	30886

prune5.1s

Filtered

1193 candidates to 924 candidates (77.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1192	1	1193
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	1193	5	1198

Merged error: 0b

Counts

1198 → 5

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
1.3b	(/ (/ (pow (cbrt (/ 1 a)) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (/ (cbrt y) x))
1.3b	(* (/ (pow (* (cbrt (/ 1 a)) (cbrt (/ 1 a))) 1.0) (* (cbrt y) (cbrt y))) (/ (/ (pow (cbrt (/ 1 a)) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (/ (cbrt y) x)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

12265×	`times-frac`
5115×	`add-sqr-sqrt`
4783×	`*-un-lft-identity`
4771×	`add-cube-cbrt`
3931×	`cbrt-prod`
2951×	`unpow-prod-down`
1853×	`associate-r`
900×	`exp-sum` `fma-udef`
397×	`div-inv`
382×	`add-exp-log`
252×	`div-exp`
215×	`sqr-pow`
135×	`prod-exp`
88×	`unswap-sqr`
84×	`associate-/l*`
67×	`add-cbrt-cube`
56×	`pow-exp`
42×	`cbrt-undiv`
38×	`pow-to-exp`
22×	`associate-/r*`
20×	`cbrt-unprod`
9×	`associate-l`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `associate-/r/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `associate-/l/`

Counts

4 → 4066

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
67.0ms	(/ (/ (pow (cbrt (/ 1 a)) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (/ (cbrt y) x))
535.0ms	(* (/ (pow (* (cbrt (/ 1 a)) (cbrt (/ 1 a))) 1.0) (* (cbrt y) (cbrt y))) (/ (/ (pow (cbrt (/ 1 a)) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (/ (cbrt y) x)))

series1.3s

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt y)
177.0ms	(cbrt y)
498.0ms	(/ (/ (pow (cbrt (/ 1 a)) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (/ (cbrt y) x))
422.0ms	(* (/ (pow (* (cbrt (/ 1 a)) (cbrt (/ 1 a))) 1.0) (* (cbrt y) (cbrt y))) (/ (/ (pow (cbrt (/ 1 a)) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (/ (cbrt y) x)))

simplify1.2s

Algorithm

egg-herbie

Counts

4078 → 4078

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5136	127740

prune27.9s

Filtered

4078 candidates to 3486 candidates (85.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	4078	0	4078
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	4078	5	4083

Merged error: 0b

Counts

4083 → 5

regimes305.0ms

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	22	12
1	22	12

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.0s	45998×	body	80	nan
1.2s	15178×	body	80	valid