Details

sample30.0ms

Algorithm

intervals

Results

9.0ms	246×	body	80	valid
3.0ms	18×	body	640	valid
2.0ms	10×	body	1280	valid
1.0ms	11×	body	320	valid
1.0ms	7×	body	160	valid

simplify89.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	116	5
3	324	5
4	861	5
5	1912	5
6	4581	5
7	5001	5

prune13.0ms

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: 10.6b

Counts

2 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.2b	(fma (/ (- y z) (- a z)) (- t x) x)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

9.0ms	(/ (- y z) (- a z))
1.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

series178.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(/ (- y z) (- a z))
121.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify70.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	265	450
1	729	425
2	2562	423
3	5002	421

prune225.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	59	11	70
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	60	12	72

Merged error: 3.6b

Counts

72 → 12

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
1.4b	(+ (* (/ (- y z) (- a z)) (- t x)) x)
1.8b	(* (/ (- y z) (- a z)) (- t x))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-sqr-sqrt`
97×	`*-un-lft-identity`
51×	`add-cube-cbrt` `times-frac`
36×	`prod-diff`
31×	`associate-l`
23×	`distribute-lft-out--` `difference-of-squares`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-r` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`sub-neg` `associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `fma-def` `frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 170

Calls

3 calls:

9.0ms	(/ (- y z) (- a z))
20.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)
18.0ms	(* (/ (- y z) (- a z)) (- t x))

series573.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(/ (- y z) (- a z))
191.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)
327.0ms	(* (/ (- y z) (- a z)) (- t x))

simplify85.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	682	1497
1	2657	1254
2	5002	1252

prune433.0ms

Filtered

179 candidates to 118 candidates (65.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	171	8	179
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	179	12	191

Merged error: 3.6b

Counts

191 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

2.0b	(cbrt (* (/ (- y z) (- a z)) (- t x)))
2.0b	(cbrt (* (/ (- y z) (- a z)) (- t x)))
2.0b	(cbrt (* (/ (- y z) (- a z)) (- t x)))
7.3b	(+ (* (* (cbrt (* (/ (- y z) (- a z)) (- t x))) (cbrt (* (/ (- y z) (- a z)) (- t x)))) (cbrt (* (/ (- y z) (- a z)) (- t x)))) x)

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-div`
6×	`frac-times` `flip3--` `associate-*r/` `flip--` `add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-prod` `pow1/3` `associate-*l/`
1×	`+-commutative` `fma-def` `flip3-+` `sum-log` `flip-+`

Counts

4 → 62

Calls

4 calls:

12.0ms	(cbrt (* (/ (- y z) (- a z)) (- t x)))
11.0ms	(cbrt (* (/ (- y z) (- a z)) (- t x)))
11.0ms	(cbrt (* (/ (- y z) (- a z)) (- t x)))
32.0ms	(+ (* (* (cbrt (* (/ (- y z) (- a z)) (- t x))) (cbrt (* (/ (- y z) (- a z)) (- t x)))) (cbrt (* (/ (- y z) (- a z)) (- t x)))) x)

series16.9s

Counts

4 → 12

Calls

4 calls:

5.6s	(cbrt (* (/ (- y z) (- a z)) (- t x)))
5.5s	(cbrt (* (/ (- y z) (- a z)) (- t x)))
5.7s	(cbrt (* (/ (- y z) (- a z)) (- t x)))
187.0ms	(+ (* (* (cbrt (* (/ (- y z) (- a z)) (- t x))) (cbrt (* (/ (- y z) (- a z)) (- t x)))) (cbrt (* (/ (- y z) (- a z)) (- t x)))) x)

simplify89.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	264	966
1	757	799
2	3079	770
3	5002	717

prune325.0ms

Filtered

74 candidates to 68 candidates (91.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	72	14	86

Merged error: 3.6b

Counts

86 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

2.0b	(cbrt (* (/ (- y z) (- a z)) (- t x)))
2.0b	(cbrt (* (/ (- y z) (- a z)) (- t x)))
2.5b	(cbrt (/ (- y z) (- a z)))
7.3b	(+ (* (* (cbrt (* (/ (- y z) (- a z)) (- t x))) (cbrt (* (/ (- y z) (- a z)) (- t x)))) (* (cbrt (/ (- y z) (- a z))) (cbrt (- t x)))) x)

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt` `*-un-lft-identity`
33×	`cbrt-prod`
25×	`times-frac`
15×	`add-cube-cbrt`
11×	`cbrt-div`
10×	`distribute-lft-out--` `difference-of-squares`
6×	`add-log-exp`
5×	`flip3--` `flip--`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `frac-times` `associate-*r/` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3`
2×	`associate-*l/` `associate-/r/`
1×	`+-commutative` `fma-def` `flip3-+` `sum-log` `flip-+` `div-inv`

Counts

4 → 88

Calls

4 calls:

12.0ms	(cbrt (* (/ (- y z) (- a z)) (- t x)))
16.0ms	(cbrt (* (/ (- y z) (- a z)) (- t x)))
7.0ms	(cbrt (/ (- y z) (- a z)))
38.0ms	(+ (* (* (cbrt (* (/ (- y z) (- a z)) (- t x))) (cbrt (* (/ (- y z) (- a z)) (- t x)))) (* (cbrt (/ (- y z) (- a z))) (cbrt (- t x)))) x)

series11.8s

Counts

4 → 12

Calls

4 calls:

5.7s	(cbrt (* (/ (- y z) (- a z)) (- t x)))
5.6s	(cbrt (* (/ (- y z) (- a z)) (- t x)))
347.0ms	(cbrt (/ (- y z) (- a z)))
199.0ms	(+ (* (* (cbrt (* (/ (- y z) (- a z)) (- t x))) (cbrt (* (/ (- y z) (- a z)) (- t x)))) (* (cbrt (/ (- y z) (- a z))) (cbrt (- t x)))) x)

simplify61.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	529	1266
1	1467	1185
2	5001	1151

prune416.0ms

Filtered

100 candidates to 85 candidates (85.0%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	1	11	12
Picked	0	1	1
Done	1	0	1
Total	100	14	114

Merged error: 3.6b

Counts

114 → 14

regimes446.0ms

Accuracy

22.8% (6.4b remaining)

Error of 10.3b against oracle of 3.9b and baseline of 12.2b

bsearch118.0ms

Steps

Iters	Range		Point
8	7.183280095972616e-88	1.620800228275719e-83	8.78383250364907e-87
8	-1.055386269196156e-138	-2.2766900434224755e-141	-9.569443762889911e-141

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	26
1	34	26

end0.0ms

sample796.0ms

Algorithm

intervals

Results

310.0ms	7797×	body	80	valid
76.0ms	488×	body	640	valid
53.0ms	296×	body	1280	valid
48.0ms	413×	body	320	valid
16.0ms	221×	body	160	valid
4.0ms	19×	body	2560	valid

Details

sample30.0ms

simplify89.0ms

prune13.0ms

localize9.0ms

rewrite13.0ms

series178.0ms

simplify70.0ms

prune225.0ms

localize11.0ms

rewrite56.0ms

series573.0ms

simplify85.0ms

prune433.0ms

localize14.0ms

rewrite68.0ms

series16.9s

simplify89.0ms

prune325.0ms

localize18.0ms

rewrite76.0ms

series11.8s

simplify61.0ms

prune416.0ms

regimes446.0ms

bsearch118.0ms

simplify2.0ms

end0.0ms

sample796.0ms

Profiling