Details

sample327.0ms

Algorithm

intervals

Results

183.0ms	102×	body	1280	valid
67.0ms	25×	body	2560	valid
41.0ms	56×	body	640	valid
10.0ms	21×	body	320	valid
7.0ms	44×	body	80	valid
2.0ms	8×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize17.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (tan (+ x eps)) (tan x))
3.1b	(tan (+ x eps))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

4×	`tan-quot` `add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `tan-sum` `frac-sub` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 25

Calls

2 calls:

27.0ms	(- (tan (+ x eps)) (tan x))
12.0ms	(tan (+ x eps))

series236.0ms

Counts

2 → 6

Calls

2 calls:

141.0ms	(- (tan (+ x eps)) (tan x))
95.0ms	(tan (+ x eps))

simplify116.0ms

Counts: 31 → 31

prune157.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan eps)))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
1.9b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-log-exp`
7×	`tan-quot`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`
1×	`+-commutative` `frac-times` `flip3-+` `times-frac` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 62

Calls

4 calls:

6.0ms	(- 1 (* (tan x) (tan eps)))
8.0ms	(+ (tan x) (tan eps))
16.0ms	(* (tan x) (tan eps))
145.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series978.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(- 1 (* (tan x) (tan eps)))
163.0ms	(+ (tan x) (tan eps))
125.0ms	(* (tan x) (tan eps))
540.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify95.0ms

Counts: 74 → 74

prune344.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.2b	(exp (- 1 (* (tan x) (tan eps))))
1.9b	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps)))))) (tan x))

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-log-exp`
7×	`tan-quot` `add-cube-cbrt`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`exp-prod` `associate-r` `associate-l`
2×	`sub-neg` `diff-log` `exp-sum` `rem-exp-log` `difference-of-squares`
1×	`+-commutative` `frac-times` `flip3--` `flip3-+` `times-frac` `exp-diff` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `sum-log` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

18.0ms	(+ (tan x) (tan eps))
23.0ms	(* (tan x) (tan eps))
24.0ms	(exp (- 1 (* (tan x) (tan eps))))
221.0ms	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps)))))) (tan x))

series1.0s

Counts

4 → 12

Calls

4 calls:

146.0ms	(+ (tan x) (tan eps))
129.0ms	(* (tan x) (tan eps))
191.0ms	(exp (- 1 (* (tan x) (tan eps))))
559.0ms	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps)))))) (tan x))

simplify103.0ms

Counts: 77 → 77

prune376.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (tan x) (sin eps)) (cos eps))
0.2b	(* (tan x) (sin eps))
0.2b	(exp (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
1.9b	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (/ (* (tan x) (sin eps)) (cos eps)))))) (tan x))

rewrite608.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt` `add-log-exp`
6×	`pow1` `exp-prod`
4×	`times-frac` `difference-of-squares`
3×	`tan-quot` `associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `exp-sum` `associate-*l/` `prod-exp` `cbrt-unprod` `rem-exp-log` `distribute-lft-out--`
1×	`flip3--` `frac-2neg` `exp-diff` `pow-prod-down` `clear-num` `-commutative` `frac-sub` `flip--` `div-inv` `associate-/l/` `associate-/l` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

17.0ms	(/ (* (tan x) (sin eps)) (cos eps))
16.0ms	(* (tan x) (sin eps))
68.0ms	(exp (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
506.0ms	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (/ (* (tan x) (sin eps)) (cos eps)))))) (tan x))

series954.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (* (tan x) (sin eps)) (cos eps))
103.0ms	(* (tan x) (sin eps))
233.0ms	(exp (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
511.0ms	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (/ (* (tan x) (sin eps)) (cos eps)))))) (tan x))

simplify34.0ms

Counts: 87 → 87

prune303.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.3b

regimes198.0ms

Accuracy

87.9% (0.9b remaining)

Error of 15.6b against oracle of 14.8b and baseline of 22.1b

bsearch162.0ms

Steps

Iters	Range		Point
7	8.407693552421027e-40	1.1586561956724652e-37	1.1326201027600925e-37
6	-1.0453104980513488e-63	-1.0982003274564392e-64	-1.0297644102132857e-63

simplify89.0ms

end0.0ms

sample11.1s

Algorithm

intervals

Results

5.9s	3342×	body	1280	valid
2.1s	1831×	body	640	valid
1.8s	644×	body	2560	valid
499.0ms	793×	body	320	valid
252.0ms	1065×	body	80	valid
154.0ms	325×	body	160	valid