Details

sample189.0ms

Algorithm

intervals

Results

79.0ms	1533×	body	80	nan
33.0ms	518×	body	80	valid

simplify52.0ms

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: 0.2b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

395×	`*-un-lft-identity`
215×	`exp-sum`
192×	`associate-r`
177×	`add-sqr-sqrt`
165×	`times-frac`
161×	`add-cube-cbrt`
135×	`prod-diff`
132×	`associate-l`
96×	`distribute-lft-out`
72×	`log-prod`
70×	`associate--l+`
55×	`associate-/l*`
40×	`distribute-lft-out--`
36×	`distribute-rgt-in` `distribute-lft-in`
30×	`associate-+l+` `associate-+r+`
15×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`exp-prod`
10×	`pow1` `add-log-exp`
6×	`*-commutative` `unswap-sqr`
5×	`+-commutative` `sub-neg`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u`
3×	`div-exp` `associate-/r*` `cbrt-unprod` `rem-exp-log`
2×	`cbrt-undiv` `exp-diff` `diff-log` `pow-prod-down` `associate-*l/` `log-pow` `difference-of-squares`
1×	`flip3--` `frac-2neg` `associate-*r/` `clear-num` `sum-log` `flip--` `div-inv` `associate-/l/`

Counts

4 → 366

Calls

4 calls:

7.0ms	(* (- t 1.0) (log a))
5.0ms	(* y (log z))
31.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
50.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series388.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (- t 1.0) (log a))
41.0ms	(* y (log z))
118.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
172.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify133.0ms

Algorithm

egg-herbie

Counts

378 → 378

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1289	5547
1	4884	4154
2	5001	4154

prune900.0ms

Filtered

378 candidates to 185 candidates (48.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	373	5	378
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	374	6	380

Merged error: 0b

Counts

380 → 6

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)))) y)
0.1b	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.1b	(fma (log (/ 1 a)) t b)
1.9b	(* (/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) y) x)

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

1295×	`times-frac`
595×	`add-sqr-sqrt`
571×	`*-un-lft-identity`
570×	`add-cube-cbrt`
445×	`unpow-prod-down`
220×	`associate-l`
178×	`associate-/l*`
140×	`fma-udef`
138×	`exp-sum`
102×	`associate-*l/`
83×	`add-exp-log`
58×	`div-exp`
48×	`associate-/l/`
44×	`div-inv`
35×	`sqr-pow`
18×	`add-cbrt-cube`
16×	`pow-exp`
14×	`prod-exp` `associate-/r*`
7×	`unswap-sqr`
6×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `pow-to-exp` `rec-exp` `frac-2neg` `1-exp` `clear-num` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `cbrt-unprod`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 722

Calls

4 calls:

30.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) y)
1.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
1.0ms	(fma (log (/ 1 a)) t b)
61.0ms	(* (/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) y) x)

series1.0s

Counts

4 → 12

Calls

4 calls:

325.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) y)
84.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
78.0ms	(fma (log (/ 1 a)) t b)
520.0ms	(* (/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) y) x)

simplify158.0ms

Algorithm

egg-herbie

Counts

734 → 734

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	2712	12135
1	5001	11734

prune3.7s

Filtered

734 candidates to 579 candidates (78.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	730	4	734
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	735	5	740

Merged error: 0b

Counts

740 → 5

localize21.0ms

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

rewrite352.0ms

Algorithm

rewrite-expression-head

Rules

4084×	`times-frac`
1776×	`associate-l`
1755×	`add-sqr-sqrt`
1731×	`add-cube-cbrt` `*-un-lft-identity`
1338×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
1274×	`unpow-prod-down`
412×	`fma-udef`
410×	`exp-sum`
191×	`associate-/l*`
170×	`neg-mul-1`
123×	`div-inv`
98×	`sqr-pow`
48×	`associate-*l/` `distribute-neg-frac`
36×	`associate-r`
24×	`associate-/l/`
18×	`associate-/r*`
12×	`*-commutative` `unswap-sqr`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`cbrt-undiv` `distribute-lft-neg-out` `div-exp` `prod-exp` `cbrt-unprod`
1×	`distribute-frac-neg` `pow-prod-down`

Counts

4 → 1988

Calls

4 calls:

31.0ms	(* (- (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) x)
1.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
1.0ms	(fma (log (/ 1 a)) t b)
84.0ms	(/ (* (- (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) x) (- y))

series907.0ms

Counts

4 → 12

Calls

4 calls:

291.0ms	(* (- (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) x)
225.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
79.0ms	(fma (log (/ 1 a)) t b)
312.0ms	(/ (* (- (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) x) (- y))

simplify475.0ms

Algorithm

egg-herbie

Counts

2000 → 2000

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5001	50589

prune10.4s

Filtered

2000 candidates to 1544 candidates (77.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	1998	2	2000
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	2000	5	2005

Merged error: 0b

Counts

2005 → 5

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite4.5m

Algorithm

rewrite-expression-head

Rules

4304402×	`times-frac`
1927753×	`add-sqr-sqrt`
1663151×	`*-un-lft-identity`
1519807×	`add-cube-cbrt`
1362080×	`unpow-prod-down`
826218×	`associate-l`
796106×	`cbrt-prod`
636116×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
250117×	`unswap-sqr`
166572×	`fma-udef`
166570×	`exp-sum`
156108×	`associate-r`
136962×	`swap-sqr`
79744×	`neg-mul-1`
43332×	`div-inv`
40157×	`sqr-pow`
29209×	`*-commutative`
21190×	`associate-/r/`
21054×	`associate-*l/`
17348×	`associate-/l*`
4068×	`associate-/r*`
642×	`frac-2neg` `clear-num`
110×	`associate-/l/` `distribute-neg-frac`
82×	`add-exp-log`
51×	`div-exp`
27×	`add-cbrt-cube`
18×	`prod-exp`
12×	`cbrt-undiv`
8×	`pow-exp`
4×	`pow1` `expm1-log1p-u` `pow-to-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`neg-sub0` `div-sub` `distribute-frac-neg`

Counts

4 → 809433

Calls

4 calls:

19.1s	(/ (- (/ (pow (/ (* (cbrt 1) (cbrt 1)) 1) 1.0) 1)) (/ (- y) (* (/ (pow (/ (cbrt 1) a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) x)))
1.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
1.0ms	(fma (log (/ 1 a)) t b)
71.0ms	(/ (- y) (* (/ (pow (/ (cbrt 1) a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

558.0ms	(/ (- (/ (pow (/ (* (cbrt 1) (cbrt 1)) 1) 1.0) 1)) (/ (- y) (* (/ (pow (/ (cbrt 1) a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) x)))
91.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
82.0ms	(fma (log (/ 1 a)) t b)
468.0ms	(/ (- y) (* (/ (pow (/ (cbrt 1) a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) x))

simplify5.1m

Algorithm: egg-herbie